Degree sum conditions for the existence of homeomorphically irreducible spanning trees

被引：4

作者：

Ito, Taisei ^{[1
]}

Tsuchiya, Shoichi ^{[1
]}

机构：

[1] Senshu Univ, Sch Network & Informat, Kawasaki, Kanagawa, Japan

来源：

JOURNAL OF GRAPH THEORY | 2022年 / 99卷 / 01期

关键词：

homeomorphically irreducible spanning tree; spanning tree;

D O I：

10.1002/jgt.22732

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In 1990, Albertson, Berman, Hutchinson, and Thomassen proved a theorem which gives a minimum degree condition for the existence of a spanning tree with no vertices of degree 2. Such a spanning tree is called a homeomorphically irreducible spanning tree (HIST). In this paper, we prove that every graph of order n ( n >= 8) contains a HIST if d ( u ) + d ( v ) >= n - 1 for any nonadjacent vertices u and v. The degree sum condition is best possible.

引用

页码：162 / 170

页数：9

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